Problem: $eg - 3f + g - 8 = -f + 5g - 5$ Solve for $e$.
Solution: Combine constant terms on the right. $eg - 3f + g - {8} = -f + 5g - {5}$ $eg - 3f + g = -f + 5g + {3}$ Combine $g$ terms on the right. $eg - 3f + {g} = -f + {5g} + 3$ $eg - 3f = -f + {4g} + 3$ Combine $f$ terms on the right. $eg - {3f} = -{f} + 4g + 3$ $eg = {2f} + 4g + 3$ Isolate $e$ $e{g} = 2f + 4g + 3$ $e = \dfrac{ 2f + 4g + 3 }{ {g} }$